Can a camera alternate between two exposure settings during a timelapse?

Sometimes, but it depends on the camera. The closest built-in feature is usually exposure bracketing: many cameras can record a sequence such as one metered frame, one underexposed frame, and one overexposed frame, and some models may support a two-shot bracket. If bracketing works during interval shooting on your camera, it can alternate exposures automatically for each timelapse frame.

However, built-in timelapse/intervalometer features often have limited control, and support for bracketing during timelapse is very model-dependent.

If your camera can’t do this natively, you would otherwise need to change settings manually, or use an external intervalometer/timelapse controller. Dedicated units often provide better control and may also support gradual exposure changes over time (often called bulb ramping or “bramping”), which can be useful in changing light.